Experimental Vs Theoretical 2fqkge5 | PDF - Free Printable
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Step-by-step solution for: Experimental Vs Theoretical 2fqkge5 | PDF
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Step-by-step solution for: Experimental Vs Theoretical 2fqkge5 | PDF
Here are the step-by-step solutions for each problem on the worksheet.
1.) What is the theoretical probability that an even number will be rolled on a number cube?
* Step 1: Identify the total possible outcomes on a standard number cube (die). The numbers are 1, 2, 3, 4, 5, and 6. So, there are 6 total outcomes.
* Step 2: Identify the "favorable" outcomes (rolling an even number). The even numbers are 2, 4, and 6. So, there are 3 favorable outcomes.
* Step 3: Write the probability as a fraction: $\frac{\text{favorable}}{\text{total}} = \frac{3}{6}$.
* Step 4: Simplify the fraction. Both numbers can be divided by 3. $\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$.
2.) What was the experimental probability of how many times an even number was actually rolled using the table?
* Step 1: Find the total number of rolls performed in the experiment. Add up all the frequencies from the table: $8 + 3 + 9 + 6 + 4 + 6 = 36$ total rolls.
* Step 2: Find how many times an even number appeared. Look at the rows for 2, 4, and 6:
* Number 2 appeared 3 times.
* Number 4 appeared 6 times.
* Number 6 appeared 6 times.
* Total even rolls = $3 + 6 + 6 = 15$.
* Step 3: Write the experimental probability: $\frac{15}{36}$.
* Step 4: Simplify the fraction. Both numbers are divisible by 3. $\frac{15 \div 3}{36 \div 3} = \frac{5}{12}$.
3.) If you roll a number cube 36 times, how many times would you expect to roll the number one?
* Step 1: Determine the theoretical probability of rolling a 1. There is only one "1" on the cube, and 6 sides total. Probability = $\frac{1}{6}$.
* Step 2: Multiply the probability by the total number of rolls to find the expected value.
* Calculation: $36 \times \frac{1}{6} = \frac{36}{6} = 6$.
4.) How many times did you actually roll the number one in the experiment?
* Step 1: Look at the frequency table provided in the image.
* Step 2: Find the row for "Number on Cube" equal to 1.
* Step 3: Read the corresponding value in the "Frequency" column. It is 8.
5.) What is the theoretical probability for rolling a number greater than 4?
* Step 1: Identify numbers on a cube greater than 4. These are 5 and 6.
* Step 2: Count the favorable outcomes. There are 2 numbers (5 and 6).
* Step 3: Count total outcomes. There are 6 sides.
* Step 4: Write the fraction: $\frac{2}{6}$.
* Step 5: Simplify the fraction. Divide top and bottom by 2: $\frac{1}{3}$.
6.) What was the experimental probability of rolling a number greater than 4?
* Step 1: Identify numbers greater than 4: these are 5 and 6.
* Step 2: Find their frequencies in the table:
* Number 5 frequency: 4
* Number 6 frequency: 6
* Total favorable rolls: $4 + 6 = 10$.
* Step 3: Use the total number of rolls calculated in question #2, which is 36.
* Step 4: Write the probability: $\frac{10}{36}$.
* Step 5: Simplify the fraction. Divide top and bottom by 2: $\frac{5}{18}$.
7.) What is the difference between theoretical and experimental probability?
* Theoretical Probability: This is what *should* happen based on math and logic (e.g., knowing a coin has two sides means there is a 50% chance of heads). It doesn't require doing an experiment.
* Experimental Probability: This is what *actually* happened when you performed a real test or experiment (e.g., flipping a coin 10 times and getting heads 7 times). It is based on real data.
8.) If a car factory checks 360 cars and 8 of them have defects, how many will have defects out of 1260?
* Step 1: Set up a proportion. We assume the rate of defects stays the same.
$$ \frac{8 \text{ defects}}{360 \text{ cars}} = \frac{x \text{ defects}}{1260 \text{ cars}} $$
* Step 2: Solve for $x$. You can cross-multiply or simplify first. Let's simplify the left side first.
$$ \frac{8}{360} = \frac{1}{45} $$ (Dividing both by 8)
* Step 3: Now solve $\frac{1}{45} = \frac{x}{1260}$.
* Step 4: Multiply 1260 by $\frac{1}{45}$ (which is the same as dividing 1260 by 45).
$$ 1260 \div 45 = 28 $$
Final Answer:
1.) 1/2
2.) 5/12
3.) 6
4.) 8
5.) 1/3
6.) 5/18
7.) Theoretical probability is what is expected to happen based on math, while experimental probability is what actually happens during a real test.
8.) 28
1.) What is the theoretical probability that an even number will be rolled on a number cube?
* Step 1: Identify the total possible outcomes on a standard number cube (die). The numbers are 1, 2, 3, 4, 5, and 6. So, there are 6 total outcomes.
* Step 2: Identify the "favorable" outcomes (rolling an even number). The even numbers are 2, 4, and 6. So, there are 3 favorable outcomes.
* Step 3: Write the probability as a fraction: $\frac{\text{favorable}}{\text{total}} = \frac{3}{6}$.
* Step 4: Simplify the fraction. Both numbers can be divided by 3. $\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$.
2.) What was the experimental probability of how many times an even number was actually rolled using the table?
* Step 1: Find the total number of rolls performed in the experiment. Add up all the frequencies from the table: $8 + 3 + 9 + 6 + 4 + 6 = 36$ total rolls.
* Step 2: Find how many times an even number appeared. Look at the rows for 2, 4, and 6:
* Number 2 appeared 3 times.
* Number 4 appeared 6 times.
* Number 6 appeared 6 times.
* Total even rolls = $3 + 6 + 6 = 15$.
* Step 3: Write the experimental probability: $\frac{15}{36}$.
* Step 4: Simplify the fraction. Both numbers are divisible by 3. $\frac{15 \div 3}{36 \div 3} = \frac{5}{12}$.
3.) If you roll a number cube 36 times, how many times would you expect to roll the number one?
* Step 1: Determine the theoretical probability of rolling a 1. There is only one "1" on the cube, and 6 sides total. Probability = $\frac{1}{6}$.
* Step 2: Multiply the probability by the total number of rolls to find the expected value.
* Calculation: $36 \times \frac{1}{6} = \frac{36}{6} = 6$.
4.) How many times did you actually roll the number one in the experiment?
* Step 1: Look at the frequency table provided in the image.
* Step 2: Find the row for "Number on Cube" equal to 1.
* Step 3: Read the corresponding value in the "Frequency" column. It is 8.
5.) What is the theoretical probability for rolling a number greater than 4?
* Step 1: Identify numbers on a cube greater than 4. These are 5 and 6.
* Step 2: Count the favorable outcomes. There are 2 numbers (5 and 6).
* Step 3: Count total outcomes. There are 6 sides.
* Step 4: Write the fraction: $\frac{2}{6}$.
* Step 5: Simplify the fraction. Divide top and bottom by 2: $\frac{1}{3}$.
6.) What was the experimental probability of rolling a number greater than 4?
* Step 1: Identify numbers greater than 4: these are 5 and 6.
* Step 2: Find their frequencies in the table:
* Number 5 frequency: 4
* Number 6 frequency: 6
* Total favorable rolls: $4 + 6 = 10$.
* Step 3: Use the total number of rolls calculated in question #2, which is 36.
* Step 4: Write the probability: $\frac{10}{36}$.
* Step 5: Simplify the fraction. Divide top and bottom by 2: $\frac{5}{18}$.
7.) What is the difference between theoretical and experimental probability?
* Theoretical Probability: This is what *should* happen based on math and logic (e.g., knowing a coin has two sides means there is a 50% chance of heads). It doesn't require doing an experiment.
* Experimental Probability: This is what *actually* happened when you performed a real test or experiment (e.g., flipping a coin 10 times and getting heads 7 times). It is based on real data.
8.) If a car factory checks 360 cars and 8 of them have defects, how many will have defects out of 1260?
* Step 1: Set up a proportion. We assume the rate of defects stays the same.
$$ \frac{8 \text{ defects}}{360 \text{ cars}} = \frac{x \text{ defects}}{1260 \text{ cars}} $$
* Step 2: Solve for $x$. You can cross-multiply or simplify first. Let's simplify the left side first.
$$ \frac{8}{360} = \frac{1}{45} $$ (Dividing both by 8)
* Step 3: Now solve $\frac{1}{45} = \frac{x}{1260}$.
* Step 4: Multiply 1260 by $\frac{1}{45}$ (which is the same as dividing 1260 by 45).
$$ 1260 \div 45 = 28 $$
Final Answer:
1.) 1/2
2.) 5/12
3.) 6
4.) 8
5.) 1/3
6.) 5/18
7.) Theoretical probability is what is expected to happen based on math, while experimental probability is what actually happens during a real test.
8.) 28
Parent Tip: Review the logic above to help your child master the concept of experimental probability worksheet answers.
